i like the idea and graphics personally i am a fan of games that base on logic and puzzles, but i didn't really get yours and abandoned after a while ... i suppose that is because time was short but you should give some initial explanation for your puzzles to get at least an idea of 'what to do' as there is a chance at the moment that players are even more lost than the character itself and give up early - like i did :o/
other point:
when your character leaves a room, it reappears in the middle of the next one, so that looks and feels a bit weird, like a teleport or something.
i suppose you can fix this easily by doing something like (pseudocode):
if (character.x - character.width <= screen.left): character.x = screen.right
... same for any exit-direction, x and y